Solve for $x$ and $y$ using elimination. ${x-2y = -8}$ ${-x-3y = -27}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-5y = -35$ $\dfrac{-5y}{{-5}} = \dfrac{-35}{{-5}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {x-2y = -8}\thinspace$ to find $x$ ${x - 2}{(7)}{= -8}$ $x-14 = -8$ $x-14{+14} = -8{+14}$ ${x = 6}$ You can also plug ${y = 7}$ into $\thinspace {-x-3y = -27}\thinspace$ and get the same answer for $x$ : ${-x - 3}{(7)}{= -27}$ ${x = 6}$